We look at the division of 582623 by 17 
Our goal is to divide 582623 by 17.

Advancing to step 1:
17 goes into 5 0 times with a remainder of 5.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Subtracting 0 from 5 leaves us with 5.
Append the next digit (8) from the dividend to 5 and continue with: 58 / 17

Advancing to step 2:
17 can be fit into 58 3 times, resulting in a remainder of 7.
The number 3 becomes the next digit in our result. 
Result so far: 3.0
If we subtract 51 from 58, we get 7.
Include the next digit (2) from the dividend after 7, then repeat: 72 / 17

Going ahead to step 3:
72 divided by 17 is 4 with a remainder of 4.
The next digit of our result is 4. 
Result so far: 34.0
Subtract 68 from 72 to get 4.
Take the next digit (6) from the dividend and append it to 4, then repeat: 46 / 17

Going ahead to step 4:
If we divide 46 by 17, we get 2 and a remainder of 12.
The number 2 becomes the next digit in our result. 
Result so far: 342.0
Subtract 34 from 46 to get 12.
Fetch the next digit (2) from the dividend, attach it to 12 and continue: 122 / 17

On to step 5:
17 goes into 122 7 times with a remainder of 3.
The number 7 becomes the next digit in our result. 
Result so far: 3427.0
The remainder is 3 after subtracting 119 from 122.
Append the next digit (3) from the dividend to 3 and continue with: 33 / 17

Moving on to step 6:
17 can be fit into 33 1 times, resulting in a remainder of 16.
Record the quotient 1 as the next digit in the result. 
Result so far: 34271.0
If we subtract 17 from 33, we get 16.
Since there are no more digits in the dividend, we add a zero to the remainder making it 160, and continue the process.

Moving on to step 7:
If we divide 160 by 17, we get 9 and a remainder of 7.
The number 9 becomes the next digit in our result. 
Result so far: 34271.9
If we subtract 153 from 160, we get 7.
Since there are no more digits in the dividend, we add a zero to the remainder making it 70, and continue the process.

Step 8:
17 can be fit into 70 4 times, resulting in a remainder of 2.
Record the quotient 4 as the next digit in the result. 
Result so far: 34271.94
Subtract 68 from 70 to get 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

Moving on to step 9:
20 divided by 17 is 1 with a remainder of 3.
Record the quotient 1 as the next digit in the result. 
Result so far: 34271.941
If we subtract 17 from 20, we get 3.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

Going ahead to step 10:
30 divided by 17 is 1 with a remainder of 13.
Put 1 as the next digit of the answer. 
Result so far: 34271.9411
If we take 17 away from 30, we end up with 13.
Since there are no more digits in the dividend, we add a zero to the remainder making it 130, and continue the process.

After the division, we end up with 34271.9411 and a remainder of 0.00013.